Category Assessment

Aug 15 2016

Mathematical Miscellany #5

Twitter can be useful for alerting one to resources / news, note the first two items.

Problem Solving – an open access (free) book which looks at research on Mathematical Problem Solving.
Problem Solving

Note this page for a large collection of free Mathematics books.

Tools for Maths Teachers J HallJonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. Note that you can show solutions for the GCSE questions – there is a link at the bottom of the page for each question.
JHall site

The page on Apps has recently been updated, there are fuller descriptions of the various apps and note the addition of Summaze2 from MEI and Sigma. A wonderful example of a free app – Maths to make you think, visually attractive and no irritating adverts trying to make you buy the premium edition!

Sumaze Integral

In Mathematical Miscellany 4, I mentioned the excellent Linar Equations Calculator; for an excellent way to illustrate the balance method of solving linear equations, try this manipulative on Mathisfun, this is very simple to use and does not require the user to log in.
Mathisfun Algebra Balance

tickUK Results 2016 – a new page has been created which I will update as A Level & GCSE results / news comes in. As I do each year, I will provide links to the results statistics and grade boundaries for the various examination boards.

Note my Twitter Examinations list. Check this for announcements / news. (You do not have to be a Twitter subscriber to use the list.)

Whilst this is Mathematical Miscellany #5 I have been writing these compilation posts for quite some time. They were at one time ‘Thoughts this week…”. Previous posts are all filed under the category (note the Category menu on the right) Mathematical Miscellany.

Jul 17 2016

Low Stakes Testing in the Mathematics Classroom

Please note – a completely new version of this presentation with many more resources and additional ideas will be presented at the BCME Conference, April 2018. Following my sessions, I will update all relevant pages

To download:
Low Stakes Testing in the Mathematics Classroom (PowerPoint File, takes a few moments to download)

Low Stakes Testing in the Mathematics Classroom (pdf)

Or use this shorter version to see the slides on the student survey on low stakes tests.
Mini Tests Colleen Young for PowerPoint
Mini Tests Colleen Young pdf version

Slides from the BERA Conference, Learning from the classroom – Practitioner research in mathematics education – July 2016

There are many hyperlinks provided in the presentation, for ease of access these are also provided below:

Further Reading

Jul 3 2016

Colourful Chi Squared!

Updating a presentation, Colour in Mathematics or pdf version, Colour in Mathematics led to a happy find…

Chi Squared examplw

When teaching the Chi Squared test I have often found that students are not always clear on their interpretation of the contributions to the test statistic. A worked example with a little colour to help where we look at the observed data. the expected probabilities and the chi squared contributions seems to work well . This exercise made me realise that a chi squared calculator I had previously recommended did not seem to be working, so fortunately I found a better one!

From Social Science Statistics this Chi Squared Calculator is for a contingency table with up to 5 rows and columns. It is very simple to use, enter the group and category names, then the data, choose the significance level and calculate.
Chi Squared Calculator 1
Chi Squared Calculator 2

A clear conclusion is then given:
The chi-square statistic is 10.2061. The p-value is .037096.
The result is significant at p < .05.

The calculator is included on the Statistics 16+ page of Calculators & Tools.

Note the many other calculators  for statistical tests  available on Social Science Statistics.

Jun 12 2016

A Level – Draft Specifications & a Statistics Qualification

The A Level Draft Specifications have now been published, including specimen papers.
Use this Twitter List to see updates from all the exam boards. As you can see @Ofqual are making announcements about accredited specifications.

For the specifications use the following links.

Further resources:
AQA Resources including a very useful Specification Summary. AQA have several very clear resources, see: Planning  Teaching and Assessment which includes the Specimen Papers and mark schemes.

Edexcel Specification & Sample Assessment Materials note the inclusion of a data set for AS and A Level.

Edexcel – Assessment support including mapping documents.

From OCR, specifications, specimen papers and other resources can all be downloaded here.
Note the option to download a zip file with the specifications and sample assessment materials.

OCR have individual subject pages with further resources:

MEI have helpfully compared Further Mathematics Specifications so you can compare the content and structure from each board.

OCR have also linked to some new sample MEI resources. These include some very nice “problem shorts” and also the use of technology to analyse large data sets.
MEI Sample Resources

OCR A Level Check In Test

OCR A Level Check In Test

I do like OCR’s check in tests for GCSE and I see a small number check in tests and lesson elements on the A Level subject pages; I assume this collection will grow.

From MEI, see this short video presentation on the new specification including the new work on large data sets.

For further reference documents and some suggested resources see A Level Reform.

For easy access to announcements regarding Maths from the examination boards, use this twitter list. (You do not have to use Twitter to access the list).

Royal Statistical Society Problem SolvingEduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also  the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

This discovery led me to a treasure trove of resources from Educas for Mathematics at all levels, including GCSE – this definitely needs further exploration!

Jun 5 2016

Assessment and Feedback in Mathematics

Some further notes and additional resources on Assessment and Feedback…

The first few slides (slides 1-15) introduce Assessment and Feedback, looking at definitions. To summarise:

Assessment and feedback is something we do every day in our classrooms. It’s a two way process, students and teachers working together. The feedback needs to be helpful to the students in that they can do something with it to improve their learning.

Some further useful reading:

The next section of the presentation (slides 16-23) concerns teacher – student relationships, so important and something which comes up continually in my own conversations with students, note section 3 on Classroom Climate and also these comments from younger (age 11-12) students. This is all about knowing our students well and creating a climate where it is OK to be stuck, there is trust between teacher and students and the students know that their teacher has their best interests at heart. To quote Dylan Wiliam:

Without that relationship, all the research in the world won’t matter.

Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

5-a-day
Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

Slides 32-38 illustrate some learning activities such as matching exercises which have built in feedback. For some useful resources for this type of activity try the following:

Teachit Maths KS3 Percentages code breaker

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free.
I have found many high quality resources here for all ages. Look at this activity on quadratic functionsfor example – this should really help understanding.

questionsThe next section (slides 39-45) is on questioning. Used wisely, well planned for questions can help us work out just what our students know.
Recommended reading and resources:

Retrieval Practice (Slides 46-49) looks at low stakes testing to help students recall information. Something I have found valuable throughout my teaching career and an area I am currently working on and will write further on in the near future. See:

Homework ideas are given on slides 50 to 53.

The next section is on marking (slides 54 to 63). See:
Test Analysis

  • Consider a question by question analysis on tests; this can be very revealing as to which topics a class has found harder.
  • Look at examiners’ reports to give advice to students about what examiners are looking for.
  • A very interesting read from the University of Oxford and the Education Endowment Foundation is A marked improvement? (April 2016)
  • Plan for marking, what are you looking for in a particular piece of work. Consider Ross Morrison McGill’s (@teachertoolkit) 5 Minute Marking Plan
  • For simple day to day marking, ask your students to assess themselves using RAG123.

Further Resources